Here is an infinite set of numbers

Suppose a logarithm function which satisfy

on the modulo N and the function is one-to-one, thus

The range of the function must be in the set of numbers

We call the set of the above conditions "cyclic logarithm condition".
For example in the case of *N*=4 (thus ),
assuming the following multiplication table

,

the function

satisfies the cyclic logarithm condition.
(E.g. according to the multiplication table,

and their logarithms have the following relation